Bakry-Emery meet Villani

2013/08/22 by Baudoin, Fabrice · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1308.4938

Abstract

We revisit Villani's approach to the study of hypocoercive diffusion operators by applying a variant of the Bakry-Émery machinery. The method relies on a generalized Bakry-Émery type criterion that applies to Kolmogorov type operators. Our approach includes as a special case the kinetic Fokker-Planck equation and allows, in that case, to recover hypocoercive estimates first obtained by Villani.

Cited by

• On the discrete Poincaré inequality for B-schemes of 1D Fokker-Planck equations in full space
• Exponential Ergodicity in Relative Entropy and L²-Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs

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